Introduction

Contamination of water sources by heavy metals is a global ecological issue resulting from human activities like surface runoff, sewage, effluent discharge, and mine drainage. These metals can accumulate in ecosystems and enter the human food chain, leading to serious health problems such as neurological disorders, organ damage, Alzheimer's disease, and cancer. Effective and precise methods for removing these metals are therefore essential. Surface adsorption is an effective method due to its simplicity, cost-effectiveness, and versatility. Utilizing agricultural waste as adsorbents is beneficial because of its efficiency, cost-effectiveness, and renewability. Chemical modification of these wastes can further enhance their adsorption capacity and offer a sustainable solution for pollutant removal. Additionally, developing mechanistic and predictive models is crucial for optimizing the adsorption process and designing high-capacity adsorbents. Machine learning methods can enhance model clarity, interpretability, and efficiency by reducing input features while maintaining prediction accuracy.

Materials and methods
In this research, rapeseed stalks were used to produce biochar and hydrochar. After harvesting, washing and drying, rapeseed stalks were ground and turned into biochar and hydrochar. The stems were placed in a furnace at 500 degrees Celsius for four hours to produce biochar. To produce hydrochar, the ground stalks were placed in Teflon containers with deionized water and in an oven at 200 degrees Celsius for four hours. After reaching room temperature, the solid particles were washed and dried at 70°C for 24 hours. The standard lead solution (1000 mg/L) was prepared with lead nitrate and deionized water and the required concentrations were prepared by dilution. The effect of different parameters such as pH, contact time, adsorbent amount and initial lead concentration on lead absorption by adsorbents was investigated. The removal efficiency and the amount of lead absorption in each step were calculated using specific relationships. The Gene Expression Programming (GEP) model, which is an evolved version of Genetic Programming (GP) and Genetic Algorithm (GA), was developed by Ferreira in 1999 based on Darwin's theory. In this study, we investigated different combinations of parameters affecting lead absorption, such as genotype, and the results of lead absorption as a phenotype
In this study, input data including parameters such as pH, contact time, initial concentration of lead, and adsorbent amount, were used, with the output data being adsorption efficiency. Lead adsorption data on biochar were used for training and lead adsorption data by hydrochar were used for testing. All data (input and output) were normalized to avoid fluctuations and correctly identify the relationships between variables. The root mean square error (RMSE) and mean absolute error (MAE), coefficient of determination (R2) were used to measure the accuracy and efficiency of the absorption efficiency prediction by the gene expression programming model.
To evaluate the effect of input parameters on Pb removal prediction using gene expression programming, sensitivity analysis was performed. In this analysis, the correlation coefficient indicates the effect of each input parameter on lead absorption. A positive correlation coefficient indicates a direct interaction between input and output, and a negative correlation coefficient indicates an inverse interaction. Also, the higher the absolute value of the correlation coefficient, the greater the effect of that parameter on the output of the model.

Results and discussion
The effect of initial lead concentration on the adsorption efficiency by hydrochar and biochar from rapeseed stems shows that as the initial concentration of lead increases, the number of lead ions in the solution rises. Each adsorbent has a limited capacity for adsorption, and when this capacity becomes saturated, the adsorption efficiency decreases. Similar studies have confirmed that while the amount of adsorbed heavy metals increases with higher initial concentrations, the removal efficiency decreases due to adsorbent saturation.The pH of the solution affects the adsorption of lead ions by the adsorbent. Increasing the pH causes functional groups on the adsorbent surface (such as carboxyl and hydroxyl groups) to dissociate more into negative ions. This increase in negative charge on the adsorbent surface enhances the electrostatic attraction for positively charged lead ions, thus increasing the adsorption efficiency. At lower pH levels, hydrogen ions compete with lead ions for adsorption sites, leading to reduced lead ion adsorption. As the pH increases, the concentration of hydrogen ions decreases and the competition lessens, resulting in increased lead ion adsorption.The amount of adsorbent used in the adsorption process has a significant impact on the adsorption efficiency. Increasing the amount of adsorbent provides more active surface area and more binding sites for lead ions. This increase in active surface area leads to higher adsorption capacity and improved adsorption efficiency.
The results of predicting lead adsorption by hydrochar and canola stem biochar using a gene expression programming model show that reducing the number of input parameters from four (contact time, initial concentration, adsorbent mass, and pH) to three parameters (contact time, adsorbent mass, and pH) improved the model's accuracy. This improvement in accuracy was observed with an increase in R² in the training phase (0.95 compared to 0.92) and in the testing phase (0.91 compared to 0.90). Further reducing the input parameters from three (contact time, adsorbent mass, and pH) to two (contact time and pH) led to an even greater improvement in prediction accuracy. This improvement was evident with an increase in R² in the training phase (0.96 compared to 0.95) and in the testing phase (0.94 compared to 0.91). Reducing input features simplified the model, leading to faster training and more accurate predictions. This approach also reduced laboratory and operational costs, decreased chemical and equipment usage, and saved time and human resources. Additionally, focusing on key parameters and eliminating unnecessary features reduced model complexity and improved prediction accuracy. These results highlight the importance of optimizing input parameters in modeling complex processes and reducing associated costs. The computed correlation coefficient for all parameters affecting lead adsorption predicted by the gene expression programming model on hydrochar and biochar showed that the parameters pH and contact time had the most positive impact on lead adsorption. On the other hand, the initial concentration of lead had an inverse effect on the adsorption process. As the initial concentration of lead increased, the number of lead ions in the solution also increased, leading to rapid saturation of the adsorbent’s capacity and a decrease in adsorption efficiency.

Conclusion
The study showed that by optimizing and reducing the number of input parameters in the gene expression programming model, the accuracy and efficiency of lead adsorption predictions could be significantly improved. Selecting the right input parameters not only simplifies the model and reduces training time but also enhances prediction accuracy and reduces overfitting. Consequently, using the two key parameters (contact time and pH) yielded the best results in the study.